GELFAND商环和正规素谱

Gelfand Factor Rings and Normal Spectra

设R是任意带单位元的结合环,specl(R)是弱Zariski拓扑空间。利用了环的素谱的一些拓扑性质去刻画Gelfand商环。对任意环R,N(R)表示环R的素根,证明了R/N(R)是Gelfand环当且仅当spec(R)∪maxl(R)是正规拓扑空间,当且仅当maxl(R)是spec(R)∪maxl(R)的保核收缩映射。

Let R be any associative ring with identity. Then specl （R） is a space with weak Zariski topology. In this paper, some Gelfand factor rings＇ equivalent conditions are proved by using some topological properties of rings. It is proved that if R is any ring and N（R ） is a prime radical of R, then R/N（R） is a Gelfand ring if and only if spec（R） ∪maxl（R） is a normal space, if and only if maxl（M） is a retract of spec（R）∪ maxl（R）.